KR20010039442A - A reconstruction method of axial power shapes in core monitoring system using virtual in-core detectors - Google Patents

Abstract

PURPOSE: An axial output distribution calculating method by using a virtual nuclear measuring instrument on the core monitoring system is provided to improve the margin of operation by reducing an axial output distribution error. CONSTITUTION: The axial output distribution calculating method includes the steps of setting the virtual incore nuclear measuring instrument, deriving the optimal correlation between the outputs of the existing real five nuclear measuring instruments and the outputs of the virtual nine nuclear measuring instruments, estimating the outputs of the virtual nine nuclear measuring instruments, calculating the 40 or 20 axial outputs by calculating the coefficients of the Fourier functions constructed by nine modes by using the estimated outputs.

Description

A reconstruction method of axial power shapes in core monitoring system using virtual in-core detectors}

The present invention relates to a core sense clock tube of a Korean standard nuclear power plant that calculates an axial output distribution using virtual in-house nuclear measuring instrument information. In particular, the present invention relates to determining output information of nine virtual nuclear measuring instruments and calculating an axial output distribution using the same. will be.

The Korea Standard Nuclear Power Plant and its subsequent reactors, which are loaded with 177 nuclear fuel assemblies, are equipped with a core watch casing to determine the core status in real time or using stored data.

The core watch case plays a role of accurately understanding the core state and warns if there is a possibility of stopping operation, based on various instrument information and calculation results. Provide information intensively.

One of the most important factors in determining the operating margin is the core mean axial power distribution.

Currently, the nuclear fuel assembly used in the Korean standard nuclear power plant has five holes the size of four nuclear fuel rods, except for the hole located at the center of the nuclear fuel assembly. In the central hole, nuclear instrument clusters with properties proportional to the distribution of neutron flux in the core are inserted to obtain data for calculating the axial power distribution. Currently, the number of Korean standard nuclear power plants is 45.

Each in-house nuclear instrument assembly has five 40 cm rhodium nuclear instruments at 10%, 30%, 50%, 70%, and 90% positions at an effective core height of 100. Is present at the reactor core, so that the core watch tube can calculate the core average axial output distribution as well as the fuel assembly axial output distribution where the nuclear instrument assembly is installed.

FIG. 1 shows how the present Korean standard nuclear reactor core is constructed and where the above-mentioned 45 furnace nuclear instrument assemblies are located in the Korean standard nuclear reactor core.

Currently, the core watch case adopts a method of synthesizing the core average axial output distribution by five Fourier functions using five axial output information obtained from the output information of these 225 fixed nuclear instruments. As the core combustion progresses, it produces an output distribution that is far from the output distribution obtained by the neutron diffusion equation.

As the output distribution is abnormally calculated, the critical variables important to the operation are overestimated among the operation information indicated by the core watch tube, which may limit the operation of the reactor despite the fact that the operation margin is sufficient.

It is an object of the present invention to provide a core mean axial output distribution calculation method using a virtual nuclear instrument to drastically reduce the core mean axial output distribution error of the existing core watch tube. .

In order to achieve the above object, the present invention introduces nine virtual nuclear instruments, and derives an optimal correlation between the actual nuclear instrument and the virtual nuclear instrumentation period in order to accurately predict the outputs of the five nuclear instrument information. Regression analysis using continuous high-order polynomials, 9 virtual nuclear instrument outputs from 5 measured nuclear instrument information using the calculated higher-order polynomials, and 9 axial outputs as inputs to synthesize nine Fourier functions. It features a series of methods to provide core mean axial power distribution.

1 is a view showing the core form of a Korean standard nuclear power plant and the installation position of 45 furnace-integrated nuclear instrument assemblies;

2 is a location diagram of five axial rhodium nuclear instruments installed in one nuclear instrument assembly;

3 is a cross-sectional view of a rhodium nucleus instrument assembly and a rhythm nucleus instrument side view.

4 shows the average axial power distribution of the 40 node cores by combustion degree calculated by the offline core watch tube based on the measured data in the 2nd cycle of Glory Unit 3.

5 is the mean axial power distribution by the core burn rate described in Yeonggwang 3 cycle 2 nuclear design report

Fig. 6 is a comparison of the mean square root error between the output distribution predicted by the existing core watch tube and the nuclear design computer code output distribution for each of the 3463 output distribution data of the 3rd and 4th cycles of the Yeonggwang 3 unit.

Figure 7 is a comparison between the virtual nuclear instrument installation position and the existing axial nuclear instrument position in accordance with the present invention

8 is a correlation diagram between the actual axial output information and the eighth virtual nuclear instrument output information according to the present invention in the 4th period of Glory Unit 3

FIG. 9 shows the distribution of the optimal transform data corresponding to the five actual axial output information and the eighth virtual nuclear instrument output information calculated by the alternate condition expected value algorithm according to the present invention in Glory No. 3 cycle. Distribution

10 is a calculation flowchart of a process of acquiring optimal deformation data using an alternate condition expected value algorithm according to the present invention.

FIG. 11 is a diagram illustrating the division of three regions of optimal transform data and a continuous polynomial approximation according to the present invention (optimal transform data corresponding to the fourth actual nuclear instrument data of the 2nd and 8th virtual nuclear instruments of Glory No. 3)

12 is a flow chart for acquiring virtual nuclear instrument output using optimally modified continuous polynomial according to the present invention.

Figure 13 is a relative comparison between the axial peak output of the five conventional Fourier function synthesis method and the axial peak output according to the present invention for the 3 cycles of Glory 3 and 4 cycles of Glory 3 according to the present invention

14 is a graph showing the axial output distribution of the 40 node core averages by combustion rate using the 2nd period measurement data of Gwanggwang Unit 3 according to the present invention.

Hereinafter, with reference to the accompanying drawings will be described in detail the methodology and procedures developed by the present invention.

First, the role of the rhodium nuclear instrument and the method of calculating the axial output distribution of the existing core watch tube will be explained.

Figure 3 shows a simplified cross-sectional view of the rhodium nucleus instrument assembly and one rhodium nucleus instrument side view.

The rhodium nucleator assembly consists of all five rhodium nucleators, two thermocouples, a background neutron meter, and their associated wires.

A thermocouple is installed on top of the nuclear instrument assembly to measure the temperature of the coolant exiting the fuel assembly, and a background neutron meter is used to compensate for the signal from the rhodium nuclear instrument.

The rhodium nucleus instrument was manufactured using the principle that rhodium 103 reacts with a neutron to Rh-104 or Rh-104m as shown in Equation 1, and then undergoes beta decay after a certain time and is converted to another nuclide, Pd-104.

Equation 1

Β DECAY (87%) of Rh ¹⁰⁴

Rh ¹⁰³ + n ¹ → Rh ¹⁰⁴ → Pd ¹⁰⁴ + β (half-life = 42 seconds)

Β DECAY at Rh ^104m (7%)

Rh ¹⁰³ + n ¹ → Rh ^104m → Rh ¹⁰⁴ → Pd ¹⁰⁴ + β (half life = 4.4 seconds)

When voltage is applied across the rhodium nucleus instrument, current flows due to electrons caused by beta decay (e ^-1 ), and the intensity of the current is proportional to the amount of electrons generated, that is, the intensity of the neutron flux. The output of the inserted fuel assembly can be determined.

The rhodium nucleus instrument determines the output of several percent to 100 percent and can be used for about three to five cycles depending on the degree of combustion of rhodium.

Once the outputs are obtained at 225 positions, the current real-time core watch tube averages these outputs in an axial direction to produce five axial outputs and uses them in the axial output distribution calculation equation represented by five Fourier functions. .

For example, since there are a total of 45 rhodium nuclear instruments located at 10% of the core effective height in the radial direction as described above, their outputs are averaged and used as axial output information values at 10% positions.

In the same manner, the output information of the axial nuclear instrument in the remaining positions is obtained in all five average core axial outputs.

Since this information is used as the input of Equation 2 below and the information is limited to five, the total core axial output distribution is represented by five Fourier functions.

Equation 2

Where a _n has a value only when n is odd, and b _n has a value only when n is even.

The output distribution expansion coefficient is obtained from Equation 3 on the condition that the integral value of Equation 2 must match the five instrument information at five instrument positions.

Equation 3

In the above Equation 3, the integral region is as follows when the effective core length is 1.

Nuclear instrument number 1 = [0.047507,0.152493],

Nuclear instrument 2 = [0.247507,0.352493],

Nuclear instrument 3 = [0.447507,0.552493],

Nuclear instrument number 4 [0.647507,0.752493],

Nuclear instrument number 5 = [0.847507,0.952493],

If the output distribution is calculated in this way, the output distribution is calculated relatively accurately at the beginning of the cycle, but the calculation error increases gradually from the middle of the cycle in which the core average axial output distribution has a saddle shape. The impossible form is shown.

FIG. 4 shows the 40 node axial output distribution obtained by the combustion degree using off-line core watch tube using 225 furnace nuclear instrument information in 2 cycles of Glory Unit 3, and FIG. 5 shows the same cycle. It describes the axial power distribution by burnup calculated by the Nuclear Design Report.

If the reference output distribution calculation method is correct, the output distribution shown in Figs. 4 and 5 should appear very similar.

4 and 5, however, the conventional output distribution calculation method using five information shows non-physical output distribution as the core combustion proceeds, and the peak power density calculated through such output distribution (PLHR, Peak Linear). It is easy to predict that the Heat Rate limit and the Departure of Nucleate Boiling Ratio (DNBR) can be overestimated, and that the operating margin will be reduced as a result.

Furthermore, the online core watch tube uses 45 rhodium nuclear instrument output information for each axial position to calculate the five axial output information, while the offline core watch tube uses the outputs of all 177 fuel assemblies. The accuracy of the core mean axial output distribution of the system is inevitably lower than that of the offline core watch tube, and thus, it is understood that a more accurate method of calculating the core mean axial output distribution in terms of securing operational margin is required.

Meanwhile, in order to obtain the output distribution of the core watchband, the boundary condition used in Equation 2 should be determined in the design cycle of the core watchbox every cycle.

The current core watch case calculates and uses boundary conditions applied to the beginning of cycle (BOC), middle of cycle (MOC), and end of cycle (EOC) separately. This is because any boundary condition cannot cover the calculation error for the entire period.

The reason is as follows.

ROCS, a core core design code, calculates about 1,200 core states in three dimensions by three combustion degrees (BOC, MOC, EOC) in consideration of core output and control rod insertion when designing the core core design. As a result, a total of 3,600 data sets consisting of 20 node core mean axial output distributions and 5 nuclear instrument outputs are obtained.

Here, the core mean axial output distribution is an output distribution obtained when the average output value of the 177 fuel assemblies at each axial position is obtained and the 20 node outputs are normalized so that the sum is 1. .

As the combustion proceeds, the axial output distribution is very different. As the cycle ends, as shown in Fig. 5, the output of the core is low and the saddle shape is high. If the boundary condition set to predict the output distribution in function form is used until the end of the cycle, the end-of-cycle output distribution error will inevitably increase.

For this reason, the existing core watch tube finds the optimal boundary condition for each combustion degree and calculates it through the following process.

First, we assume an arbitrary boundary condition for each combustion degree, and use the given boundary condition to extract 20 node output distributions using Equation 3 from the output data of five axial nuclear instruments given in the data set. After calculating, the output of each node is compared with the ROCS output to find the root-mean-square error (RMS) for 20 nodes.

Using the same method, we obtain about 1,200 RMS values for one combustion section and average them to obtain the average axial power distribution error by Fourier Fitteing.

Since the average axial output distribution error increases or decreases according to the boundary conditions, look at the variation of the average axial output distribution error while varying the boundary conditions, and when the value becomes minimum, use the boundary condition used at that combustion interval. Set to the optimal boundary condition.

Therefore, different optimal boundary conditions for each BOC, MOC, and EOC are obtained according to the aforementioned output distribution variation.

FIG. 6 is a diagram showing the mean square root error between the neutron diffusion equation solution, that is, the ROCS calculation result and the conventional Fourier fitting synthesis solution, for the 3rd and 4th periods of Yeonggwang Unit 3. Increasingly, the error of the Fourier fitting solution is large.

The output distribution error and abnormal output distribution prediction caused by the lack of information have been introduced in the present invention to solve the problems of the existing core watch case axial virtual nuclear instrument.

7 is an axial comparison of the position and size of the existing nuclear instrument position and virtual nuclear instrument position.

The virtual nuclear instrument is 38.1 cm long (which corresponds to the length of two nodes when the core effective height is equal to 20 equal to 381 cm), five in the axial direction of the existing nuclear instrument, and one between the existing nuclear instrument. It is assumed that there are four, nine virtual rhodium nucleators in total.

In addition, it is assumed that the virtual nuclear instrument assembly is installed in all nuclear fuel assemblies.

Therefore, when calculating the core mean axial output distribution, the average output of 177 fuel assemblies for each axial position is conceptually the virtual nuclear instrument output information at that position.

This is more accurate calculation of output distribution with the introduction of virtual nuclear instrument when the current core watch tube calculates core average axial output distribution using 45 nuclear instrument output average values for each axial position as axial output information. You can expect this to be possible.

On the other hand, even where a conventional rhodium nuclear instrument is installed, a virtual nuclear instrument is installed because, first, as shown in FIG. 7, the conventional nuclear instrument is 40 cm, which produces a different output from the 38.1 cm long virtual nuclear instrument.

The question is how to correctly construct nine virtual nuclear instrument information from five real in-house nuclear instrument information.

The present invention has developed a method for easily obtaining an optimal correlation between five nuclear instrument information and individual virtual nuclear instrument information using a statistical method. Once nine virtual nuclear instrument information is obtained, the existing five Fourier By using nine Fourier functions instead of functions, the core mean axial output distribution can be obtained, which not only enables more accurate output distribution simulations, but also ensures sufficient accuracy with only one boundary condition.

Using statistical methods requires a lot of basic data.

Although plant survey data are themselves excellent basic data, they only provide information on nuclear instrumentation and the output calculated by current core watchdogs, but cannot accurately determine the exact distribution of neutron distribution.

Therefore, the above data is used for verifying the core average output distribution type, and the optimal correlation is obtained by using a total of 3,600 core simulation data sets calculated every cycle by the nuclear design code ROCS.

First, since the ROCS computational code lacks the concept of a virtual nuclear instrument, it cannot provide information about it, so nine virtual nuclei from the normalized 20 node core average axial outputs remain unchanged, while leaving five nuclear instrument information contained in over 3,600 ROCS result sets. Calculate the output of the instrument position.

For example, the first virtual nuclear instrument, located at 10% of the effective core height, spans the second and third of the 20 axial nodes of the ROCS (see Figure 7), so add these outputs to the output of the virtual nuclear instrument. .

Similarly, the second virtual nuclear instrument output is the sum of the outputs of nodes 4 and 5, the eighth virtual nuclear instrument output is the sum of the outputs of nodes 16 and 17, and the ninth virtual nuclear instrument output is the output of nodes 18 and 19. Calculate by adding up.

The difference between the virtual nuclear instrument output and the five nuclear instrument output information is summarized as follows.

The five real-time nuclear instrument information produced by ROCS three-dimensional calculations was obtained by averaging only the output of 45 nuclear fuel assemblies inserted with the nuclear instrument out of the outputs of 177 radial fuel assemblies, whereas the 20-core core mean axial output distribution was Since it is obtained by normalizing the output information of all 177 fuel assemblies for each axial position, the outputs of nine virtual nuclear instruments obtained from the 20 node core average axial outputs are representative of the 177 fuel assembly output information of the positions. The result is a more accurate representation of the core mean axial power distribution than actual data representing only 45 fuel assemblies.

This is precisely in line with the original assumption that nine virtual nuclear instruments were installed in each fuel assembly and the axial virtual instrument output information was the same as the average output of 177 virtual nuclear instruments.

In this way, if all nine virtual instrument information is obtained from the 20 node core mean axial output distribution, a total of 3,600 new data sets are generated along with the five actual nuclear instrument output information.

We will now discuss how each of the virtual nuclear instruments correlate with the five actual nuclear instrument signals and explain in detail the process of making them easier to handle in the core watch tube.

In order to obtain the optimal correlation between five real nuclear instrument signals and the output of one virtual nuclear instrument by a conventional statistical method, first assume an initial function and then obtain a correlation through several conversion processes. You have to go through the process of changing the initial function repeatedly.

Furthermore, since the data set we are dealing with is a multivariate regression problem with five independent variables and one dependent variable, the initial function is not easy to set because the data itself is very diffuse.

8 shows the relationship between the output of the eighth virtual instrument and the outputs of each of the five real nuclear instruments, as the 4th and 5th rhodium nuclei where the positions of the 8th virtual instrument are actually installed. Since they exist between instruments, they have a nearly proportional relationship to them, and are inversely related to the first and second real nuclear instruments.

The above observations are exactly the same in terms of reactor neutron behavior.

It can be seen that there is a somewhat diffuse relationship with the third actual rhodium nuclear instrument, which means that even if the core top output changes a lot, the core output of the core is relatively unchanged, so it is difficult to see a proportionality or inverse relationship. It means that it is not easy to identify the last name.

In addition, although the 8th virtual instrument output information is proportional to the 4th and 5th actual nuclear instrument output, there is a difference in slope according to the combustion degree, and as the value of the nuclear instrument output information increases, the 8th virtual instrument output information gradually increases. As it is shown in a distracting form, when performing the existing statistical regression analysis, it can be expected that not only the initial function assumption is easy but also several iterations are required.

Therefore, in the case of using the existing statistical method, cumbersome repetition calculations and user judgments are important, and as a result, it may be very difficult to determine the optimal correlation.

The present invention uses an Alternate Conditional Expectation Algorithm (hereinafter, referred to as an ACE algorithm) that can obtain an optimal correlation of a multivariate problem without user judgment or intervention.

This method was developed in 1985 by L. Breiman and JHFridman and published in the American Statistical Society, where it is difficult to directly solve a given multivariate regression problem, transforming these variables and optimizing the correlation between them. This is a very useful multivariate regression algorithm developed recently among many researches on statistical techniques for deriving optimal correlations between existing multivariables, and whether a transformed function exists and whether it can be easily approximated with a known function. This is a great way to answer the fundamental question.

In the nuclear field, in 1995, H.G.Kim and J.C.Lee used the ACE algorithm for the first time in predicting critical heat flux correlations.

The equations basically used in the ACE algorithm are summarized in equations (4), (5) and (6).

Equation 4

Equation 5

Equation 6

In Equations 4, 5, and 6, Dn denotes the nth actual nuclear instrument output, Pv denotes the vth virtual nuclear instrument output, φn and θ denote optimal deformation variables corresponding to Dn and Pv, respectively, and S Means that the conditional expected value is used to calculate the left-hand terms of Equations 4 and 5 at each given position.

Equation 6 is used to check whether the equations 4 and 5 converge.

In addition, the transformation variables used in Equations 4 and 5 must satisfy the condition that the average value should be 0, and the optimal variation of the virtual nuclear instrument output should satisfy the condition that the normalized value should always be used.

If the relation of Equation 6 is satisfied, i.e., if the calculation error converges within a user-specified error range, the optimal transformation variables calculated by Equations 4 and 5 have a mathematically optimal correlation, and thus, Knowing the measured nuclear instrument information and the corresponding optimal strain parameters, the inverse function of θ can be obtained from Equation 6 to simply find the output of the virtual nuclear instrument.

As a method for evaluating conditional expectation, there are a histogram, a nearest neighbor, a kernel, a regression, a supersmoother, etc. The present invention uses a kernel method.

Kernel method uses weighting function to calculate conditional expectation value. It gives weighting value of 1 for data at the location where condition expectation is to be calculated and 0 for data that is far from it. As a function that fits this principle, the Tricube function represented by Equation 7 is used.

Equation 7

In Equation (7), M is a constant designated by the user to assign a weight according to Equation (7) with respect to data in a certain section.

On the other hand, in calculating the condition expected value in order to calculate the optimal strain point of the left side i position of Equations 4 and 5, when only the simple weighted average of the [iM, i + M] interval is obtained, the convergence becomes late and a calculation error may occur. According to the existing research results, we applied the method of finding the optimal strain point of point i through linear regression within this interval.

For example, the above description may be summarized as Equation 8 for the virtual nuclear instrument.

Equation 8

In Equation 8, the first term on the right side denotes a normal weighted expectation value, and the first part of the second term denotes covariance and variance between the virtual nuclear instrument signal and its optimal strain in the [i-M, i + M] section.

In the presently published research paper, only an explanation or calculation flow of the ACE algorithm is presented. In the present invention, a computer program using the FORTRAN 90 language, DAVID (Data Analyser for Virtual In-core Detectors), is applied to apply the ACE methodology to a real problem. ) Developed independently.

The DAVID program receives the data set consisting of about 3,600 datasets mentioned above, namely 5 nuclear instrument information and 9 virtual nuclear instrument output information, and 5 actual nuclear instrument information variables and one virtual nuclear instrument output variable. According to the ACE algorithm, cross-calculation is performed while performing the cross-calculation until the error between the deformation variable of the virtual nuclear instrument output variable and the deformation variable of the five actual nuclear instrument information variables is minimized or no longer reduced. The 3,600 points are calculated.

10 is a modification of the variable five nuclear instrument variable output information that shows the calculation flow of the program _{DAVID, φ 1, φ 2, ····} φ 5, and more than 3,600 for modified function, θ, each virtual Nuclear Instruments The final value of is printed.

However, the above results cannot be applied to the actual output distribution calculation.

Given the actual output of the actual instrument, if the data is tabulated and the virtual nuclear instrument output information is obtained through interpolation or extrapolation, all 3,600 data for each variable are needed. This method requires not only 1.6MB of computational memory but also requires a lot of computation time because data must be compared for interpolation and extrapolation.

In order to solve this disadvantage, the present invention divides each variable and its corresponding transformation into three regions and approximates the data of each region by a higher-order polynomial that is a continuous function.

FIG. 11 shows how the above three sections or regions are distinguished through the relationship between the fourth nuclear instrument output information, the transformation variables thereof, and the relation φ _4. It is obtained using the Least Square Method, and the first and third sections are linearly approximated by a linear equation to obtain appropriate virtual nuclear instrument output information even when the measured nuclear instrument signal is outside these areas.

The division is automatically determined by the DAVID computer code by examining the variation of the relevant variable.In the case of the first section, as shown in FIG. 11, the first linear P1 to the arbitrary point P2 are linearly determined. The first regression analysis is performed repeatedly by moving the position of P2 from side to side until the approximate and error between the first linear approximation point and the corresponding ACE data point (circular points in FIG. 11) is within the set value. Determine.

Similarly, the third section is determined by changing the P3 for the arbitrary point P3 and the final point P4 and selecting the appropriate P3 through linear linear approximation as in the first section.

The second section is the starting point of P2 and P3. In this case, the regression analysis is performed by the least-squares method from 2nd order up to 9th order polynomial. If the mean error is within the range set by the user, the lowest order polynomial is not. If not, select the polynomial with the smallest mean error and use it as an approximation function for the second interval.

This approximation,

First, because it is a continuous function, it can provide reliable virtual nuclear instrument output information even when any five nuclear instrument signals that are not used in regression analysis are received.

Second, six sets of optimal strain variables are composed for one virtual nuclear instrument, and if each of them is divided into three sections, 16 coefficients per one optimal strain variable (three in the first section and up to ten in the second section) In total, 96 pieces of information are needed for one virtual nuclear instrument, but only 0.4% of computational memory is required compared to the table of optimal variable data.

Third, since it is expressed as a polynomial, it is possible to quickly calculate without interpolation and extrapolation, so that the calculation time is not a problem even when applied to the online core monitoring system.

Therefore, six sets of optimal strain data are obtained for one virtual nuclear instrument, and the optimal strain continuous polynomial is calculated by performing region approximation as described above for each.

12 briefly illustrates a process of acquiring virtual nuclear instrument information when all of the optimally modified continuous polynomials are calculated as described above.

For example, given any five measured nuclear instrument information, d ₁ , d ₂ ,..., And d ₅ , the yth virtual instrument output information is first shown in each of these actual nuclear instrument information as shown in the upper right of FIG. The optimal deformation polynomial corresponding to Call all of them, calculate the area to which the actual nuclear instrument output information belongs, and substitute the optimal transformation polynomial

Calculate

And the condition of Equation 6, i.e., the sum of the optimal deformation polynomials is equal to the optimal deformation of the output of the y th virtual nuclear instrument. Calculate and find its inverse, or If the optimal strain continuous polynomial is obtained by the form, P _y is determined by the function relation equation.

Therefore, if the same calculation is repeated for the remaining eight virtual nuclear instruments using the five measured nuclear instrument information, nine virtual nuclear instrument output distributions corresponding to the measured nuclear instrument output information are obtained.

So far, we have described the statistical method and the processing method that can provide accurate 9 virtual nuclear instrument output information from the five measured nuclear instrument output information.

Hereinafter, a method of deriving the continuous axial output using the nine virtual nuclear instrument output information by the above method will be described.

In the present invention, the Fourier function is used as it is in order not to modify the existing core watch case as much as possible.

However, although the conventional core watch tube used only five output information, the present invention uses nine output information. Accordingly, the size of the right side matrix of Equation 3 increases from (5 × 5) to (9 × 9). The difference is that we use the direct numerical solution, the LU (LU) decomposition, to quickly compute the matrix.

Since nine pieces of information exist, equation (3) is described again by equation (9).

Equation 9

In the above Equation 9, the integration region of each virtual nuclear instrument is sequentially [0.05, 0.15], [0.15, 0.25], [0.25, 0.35], [0.35, 0.45], [0.45, 0.55] ], [0.55, 0.65], [0.65, 0.75], [0.75, 0.85] and the 9th virtual nuclear instrument is [0.85, 0.95].

According to Equation (9), the axial output distribution is described again as in Equation (10).

Equation 10

On the other hand, since the boundary condition shown in the right side term of Equation 10 is obtained from the optimal deformation polynomial obtained from nine virtual nuclear instrument information for the whole cycle, logically only one boundary condition is required in the present invention. .

Calculating the boundary conditions is the same as the conventional method.

First, the boundary conditions are assumed, and 3,600 ROCS axial output distributions are compared with the output distributions obtained by the method according to the present invention, respectively, to find the root mean square error of the individual output distributions. Iterative calculation is performed while changing the boundary condition.

When applying the method of the present invention to the output distribution calculation, to see how accurate output distribution can be obtained by comparing the output distribution error obtained using only the existing five nuclear instrument information, Glory No. 3 cycles 1 to 4, Glory 3 Numerical experiments were performed on three-cycle and four-cycle data, and the mean square root error, the maximum square root error, the average peak output error, and the maximum peak output error were compared, respectively. The maximum square root error refers to the maximum of 3,600 square root errors, and the average peak output error is the peak output by comparing the maximum value by the ROCS maximum value with the existing method and the present method for one output distribution. After calculating the error, it means that the average value of 3,600 peak output errors is obtained.The maximum peak output error is 3,600 points. It means the maximum value of the peak output error, each represented by the equation (11).

Equation 11

In Equation 11, the superscript CAL is a calculated value and means 20 node outputs calculated by the existing 5 nuclear instrument processing method or the new 9-point processing method, and the subscript j refers to the node 1 to 20. Changes up to

The superscript ROCS is a reference value, and k in the subscript means the number of data and (k Max) means the maximum output of the kth 20 node output distribution data.

In order to directly confirm the improvement of the calculation accuracy according to the present invention, numerical calculations were performed for Yeonggwang Unit 3 to 4, Yeonggung Unit 3 and 4 cycles.

The mean square root error decreased from 2.84% to 1.03% using only five nuclear instrument information, and the maximum square root error decreased from 10.00% to 3.07% for 3,472 data. The average peak power error decreased from 3.01% to 0.08%, and the maximum peak power error decreased from 6.37% to 3.45%, respectively.

A hypothetical xenon oscillation at the 50% and 80% output conditions of Glory Unit 3's 2 cycle period to ensure that the optimal correlation polynomial, which is the key point of the present invention, can be sufficiently accurate even when the data set is not used at all. (Xenon Oscillation) was simulated by ROCS, and the axial output distribution and nuclear instrument information were obtained hourly, and then the accuracy of each method according to the existing method and the present invention was examined using this information. The mean square root error, maximum square root error, average peak power error, and maximum peak power error were 2.10%, 3.18%, 1.82%, and 3.47%, respectively. Lowered to 2.65%, 0.57% and 1.63%, and the average root mean error was 51%, the maximum root mean error was 56% Peak output error was reduced by 72.4%, and the maximum peak power error is 67%.

This result is an example showing that the output distribution using the virtual nuclear instrument according to the present invention agrees well with the solution of the neutron diffusion equation. As it has cosine function, it can be expected to show more accurate output distribution in the middle of cycle or at the end of cycle than the method used in current core watch case.

In the numerical experiments of 3,468 data sets of 3 cycles of Glory Unit 3, the four factors calculated by the existing methods were reduced by 65%, 55%, 70%, and 42%, respectively. Decrease was also observed in Glory 3, Cycle 4, and Glory 4, Cycle 3.

For example, for the Glory 4 cycle, the average square root error, maximum square root error, average peak power error, and maximum peak power error of the existing method were 2.46%, 10.97%, 2.53%, and 6.54% for 3,468 data sets. When applied to the results of the reduction of 63%, 58%, 66% and 46% respectively 0.92%, 4.60%, 0.87% and 3.54% was confirmed that the accuracy of the axial output distribution according to the present invention.

The axial peak output predictive ability and the axial peak output predictive ability of the existing core watch tube according to the present invention are important for securing the thermal margin in the future, which means that the axial peak output is the peak linear heat rate. This is because it greatly affects.

FIG. 13 compares the five conventional Fourier function synthesis methods and the axial peak outputs calculated by the method of the present invention in the glory 3rd unit 3 cycles and the 4th cycle 4th cycle.

In the above comparison, the positive value means that the existing core watch tube predicts the axial peak output higher than the axial peak output obtained by the method according to the present invention, which is about 3,500 obtained by combining five Fourier functions. This is because it is set as axial peak output.

Figure 13 shows that at least about 75% of the total figure has a positive value, which means that in both cycles, the existing core watch case will predict a higher axial peak output than at least about 75% than the method according to the present invention. Recalling that there is a possibility, and recalling that the method according to the present invention reduced the peak output calculation error by about 70% compared to the ROCS results, it is well understood that the present invention is sufficient to further secure the thermal margin in the future. have.

On the other hand, even in the verification through the measurement data, the output distribution calculation accuracy due to the present invention was confirmed.

In fact, comparing and verifying data from actual data shows that there is no ROCS calculation result. In fact, the accuracy of the two calculation methodologies cannot be compared absolutely.

However, since most of the data were obtained during normal operation at 100% power, the methodology of the report shows how the output distribution tendency of each combustion point calculated by the two methodologies is similar to the core mean axial power distribution for each combustion recorded in the nuclear design report. There is no choice but to determine the accuracy.

Based on these criteria, CECOR, an off-line core watch tube that uses all the information of 225 fixed nuclear instruments in the furnace, uses the same axial nuclear instrument data for 20 core analysis data that were performed at regular intervals during the 2nd period of Glory III. As a result of comparing the calculated axial output distribution with the output distribution obtained by applying the present invention, the output distribution of the offline core watch tube appears abnormally toward the end of the cycle, whereas the output distribution according to the present invention is compared with the output distribution predicted by the ROCS. It can be seen that similar calculations.

FIG. 14 is an example of the above description, and each combustion point obtained by using nine virtual nuclear instruments using the axial power distribution obtained at five combustion points and the measured nuclear gauge information obtained at the same combustion point. Figures comparing the output distribution of.

The accuracy of the output distribution calculation method according to the present invention can be seen by comparing FIG. 5 with the axial output distribution according to the two-cycle combustion degree of Glory No. 3 given in FIG. 14.

The best-fit polynomial can be calculated with only one period of data, but can be calculated for several periods of data.

For example, if the optimal polynomial is calculated using DAVID code for three period data, it can be used without modifying the optimal polynomial coefficient value over three periods, but the calculation error for each period is calculated using the individual periodic data. It is slightly increased compared to one case and the time required for regression analysis is very long, and entering a new cycle requires not only to verify the previous best-fit polynomial coefficients, but also if the core conditions, such as the use of new fuel, differ from the previous cycle, There is no great value because you do not have to use it.

As described above, the present invention can have the following effects.

First, as more accurate axial output distribution calculation becomes possible during normal operation, the calculation of linear heat rate limit and DNBR limit, which determine the operation margin, become accurate and accordingly As the degree is improved, it is possible to benefit from the improvement of nuclear power utilization rate.

In addition, the operation range such as control rod insertion is increased compared to the existing method at the beginning of the reactor or at the end of the cycle when the output reactor is severely distorted. Since the above four factors are reduced by approximately 50% and used in the uncertainty evaluation, it is possible to secure additional thermal margin, thereby improving the overall reliability of the core watch tube.

Further securement of thermal margin means higher operating power, and the method developed with the present invention can bring economic benefits since it can be continuously applied until the end of the reactor life.

The technology developed by the present invention can also be applied to improve the accuracy of calculation of the axial output distribution of the reactor core protection system in the future, which can contribute to enhancing the reliability of the core protection system.

The present invention can be applied with little modification to the current core watch case. Using the developed DAVID computer code, the user can use the optimally modified polynomials for nine virtual nuclear instruments using data used for the statistical uncertainty assessment of the core watch case. It can be produced immediately without intervention, placing little burden on the designer of the core watch case.

Claims (13)

In order to improve the accuracy of calculating the axial output distribution of the core watch tube, the virtual nuclear instrument is introduced to calculate the output distribution. Obtaining a virtual nuclear instrument configuration and output information; And a second process for calculating the axial output distribution according to the output information. The method of claim 1, The first step is a axial output distribution calculation method using a virtual nuclear instrument, characterized in that nine equally installed 38.1 cm long nuclear nuclear instrument in the core. The method of claim 1, The first process is a method for calculating the axial output distribution using a virtual nuclear instrument, characterized in that all the data is used without discriminating about 3,600 core output information used for the core watchdog statistical uncertainty evaluation according to the combustion degree. The method of claim 3, wherein Using the approximately 3,600 core outputs used to evaluate the statistical uncertainty of the core watch box, the alternate condition expected value, which is a statistical method, is used to derive the optimal correlation between the nuclear instrument outputs installed in the core and the outputs of the nine virtual nuclear instruments. Axial output distribution calculation method using a virtual nuclear instrument, characterized in that using the ACE) algorithm. The method of claim 3, wherein The optimal deformation data is calculated using a DAVID code Axial Output Distribution Calculation Method Using Virtual Nuclear Instrument. The method of claim 4, wherein The ACE algorithm is an axial output distribution calculation method using a virtual nuclear instrument, characterized in that using a kernel method using a weighted function in calculating the condition expected value. The method of claim 4, wherein In the processing of the optimal strain data, the optimal strain data produced are tabulated as they are, and the output of the virtual nuclear instrument is determined by interpolation or extrapolation. Axial Output Distribution Calculation Method Using Virtual Nuclear Instrument. The method of claim 4, wherein A method of calculating the axial output distribution using a virtual nuclear instrument, characterized in that the optimal deformation data produced in the processing of optimal deformation data are divided into several sections, and each section is approximated by an arbitrary continuous function or a polynomial polynomial for each section. The method of claim 6, Axial output using a virtual nuclear instrument that calculates the condition expected value by calculating a conditional expectation value at an arbitrary position through linear linear regression analysis within a user-defined interval and obtaining a simple weighted average at the same position. Distribution calculation method. The method of claim 4, wherein Compute the optimal strain polynomial value for each measured nuclear instrument output and make the sum coincide with the optimal strain polynomial value of the virtual nuclear instrument output information to calculate the virtual nuclear instrument output directly or output the virtual nuclear instrument through the inverse function of the polynomial. Axial output distribution calculation method using a virtual nuclear instrument, characterized in that for calculating. The method of claim 1, The second process is to calculate the axial output distribution using the virtual nuclear instrument, characterized by calculating the axial output distribution with the Fourier function of nine modes using the nine virtual nuclear instrument output information obtained from the five actual output information Way. The method of claim 11, Characterized in that only one boundary condition is used throughout the period. Axial Output Distribution Calculation Method Using Virtual Nuclear Instrument. The method of claim 12, The boundary condition is the axial output distribution using the virtual nuclear instrument, characterized in that the output distribution calculated by the 9-mode Fourier function with the input of the virtual nuclear instrument output is determined to be the minimum of the root mean square error as compared to the ROCS result. Calculation method.